Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T18:40:45.888Z Has data issue: false hasContentIssue false

Experimental method to account for structural compliance in nanoindentation measurements

Published online by Cambridge University Press:  31 January 2011

J.E. Jakes*
Affiliation:
Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706; and United States Department of Agriculture (USDA) Forest Products Laboratory, Madison, Wisconsin 53726
C.R. Frihart
Affiliation:
United States Department of Agriculture (USDA) Forest Products Laboratory, Madison, Wisconsin 53726
J.F. Beecher
Affiliation:
United States Department of Agriculture (USDA) Forest Products Laboratory, Madison, Wisconsin 53726
R.J. Moon
Affiliation:
United States Department of Agriculture (USDA) Forest Products Laboratory, Madison, Wisconsin 53726
D.S. Stone
Affiliation:
Materials Science Program, University of Wisconsin—Madison, Madison, Wisconsin 53706; and Department of Materials Science and Engineering, University of Wisconsin—Madison, Madison, Wisconsin 53706
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

The standard Oliver–Pharr nanoindentation analysis tacitly assumes that the specimen is structurally rigid and that it is both semi-infinite and homogeneous. Many specimens violate these assumptions. We show that when the specimen flexes or possesses heterogeneities, such as free edges or interfaces between regions of different properties, artifacts arise in the standard analysis that affect the measurement of hardness and modulus. The origin of these artifacts is a structural compliance (Cs), which adds to the machine compliance (Cm), but unlike the latter, Cs can vary as a function of position within the specimen. We have developed an experimental approach to isolate and remove Cs. The utility of the method is demonstrated using specimens including (i) a silicon beam, which flexes because it is supported only at the ends, (ii) sites near the free edge of a fused silica calibration standard, (iii) the tracheid walls in unembedded loblolly pine (Pinus taeda), and (iv) the polypropylene matrix in a polypropylene–wood composite.

Type
Articles
Copyright
Copyright © Materials Research Society 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Oliver, W.C.Pharr, G.M.: Improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564 1992CrossRefGoogle Scholar
2Wimmer, R., Lucas, B.N., Tsui, T.Y.Oliver, W.C.: Longitudinal hardness and Young’s modulus of spruce tracheid secondary walls using nanoindentation technique. Wood Sci. Technol. 31(2), 131 1997CrossRefGoogle Scholar
3Wimmer, R.Lucas, B.N.: Comparing mechanical properties of secondary wall and cell corner middle lamella in spruce wood. IAWA J. 18(1), 77 1997CrossRefGoogle Scholar
4Gindl, W., Gupta, H.S.Grunwald, C.: Lignification of spruce tracheid secondary cell walls related to longitudinal hardness and modulus of elasticity using nano-indentation. Can. J. Bot. 80(10), 1029 2002CrossRefGoogle Scholar
5Gindl, W., Gupta, H.S., Schoberl, T., Lichtenegger, H.C.Fratzl, P.: Mechanical properties of spruce wood cell walls by nanoindentation. Appl. Phys. A: Mater. 79(8), 2069 2004Google Scholar
6Tze, W.T.Y., Wang, S., Rials, T.G., Pharr, G.M.Kelley, S.S.: Nanoindentation of wood cell walls: continuous stiffness and hardness measurements. Composites Part A: Appl. Sci. 38(3), 945 2007CrossRefGoogle Scholar
7Gindl, W.Gupta, H.S.: Cell-wall hardness and Young’s modulus of melamine-modified spruce wood by nano-indentation. Composites Part A: Appl. Sci. 33(8), 1141 2002CrossRefGoogle Scholar
8Gindl, W., Schoberl, T.Jeronimidis, G.: The interphase in phenol-formaldehyde and polymeric methylene di-phenyl-di-isocyanate glue lines in wood. Int. J. Adhes. Adhes. 24(4), 279 2004CrossRefGoogle Scholar
9Konnerth, J.Gindl, W.: Mechanical characterisation of wood-adhesive interphase cell walls by nanoindentation. Holzforschung 60(4), 429 2006Google Scholar
10Zickler, G.A., Schoberl, T.Paris, O.: Mechanical properties of pyrolysed wood: a nanoindentation study. Philos. Mag. 86(10), 1373 2006CrossRefGoogle Scholar
11Franco, G.E.L., Stone, D.S., Blank, R.D.: (unpublished work, 2005)Google Scholar
12King, R.B.: Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23(12), 1657 1987CrossRefGoogle Scholar
13Stone, D.S.: Elastic rebound between an indenter and a layered specimen. I. Model.: J. Mater. Res. 13(11), 3207 1998Google Scholar
14Stone, D.S., Yoder, K.B.Sproul, W.D.: Hardness and elastic modulus of TiN based on continuous indentation technique and new correlation. J. Vac. Sci. Technol., A 9(4), 2543 1991CrossRefGoogle Scholar
15Yoder, K.B., Stone, D.S., Hoffman, R.A.Lin, J.C.: Elastic rebound between an indenter and a layered specimen. II. Using contact stiffness to help ensure reliability of nanoindentation measurements. J. Mater. Res. 13(11), 3214 1998CrossRefGoogle Scholar
16Choi, Y., Van Vliet, K.J., Ju, L.Suresh, S.: Size effects on the onset of plastic deformation during nanoindentation of thin films and patterned lines. J. Appl. Phys. 94(9), 6050 2003Google Scholar
17Soifer, Y.M., Verdyan, A., Kazakevich, M.Rabkin, E.: Edge effect during nanoindentation of thin copper films. Mater. Lett. 59(11), 1434 2005CrossRefGoogle Scholar
18Ge, D., Minor, A.M., Stach, E.A., Morris, J.W. Jr.Size effects in the nanoindentation of silicon at ambient temperature. Philos. Mag. 86(25), 4069 2006CrossRefGoogle Scholar
19Hodzic, A., Stachurski, Z.H.Kim, J.K.: Nano-indentation of polymer-glass interfaces. I. Experimental and mechanical analysis. Polymer 41(18), 6895 2000CrossRefGoogle Scholar
20Downing, T.D., Kumar, R., Cross, W.M., Kjerengtroen, L.Kellar, J.J.: Determining the interphase thickness and properties in polymer matrix composites using phase imaging atomic force microscopy and nanoindentation. J. Adhes. Sci. Technol. 14(14), 1801 2000CrossRefGoogle Scholar
21Lee, S-H., Wang, S., Pharr, G.M.Xu, H.: Evaluation of interphase properties in a cellulose fiber-reinforced polypropylene composite by nanoindentation and finite element analysis. Composites Part A: Appl. Sci. 38(6), 1517 2007CrossRefGoogle Scholar
22Fischer-Cripps, A.C.: Critical review of analysis and interpretation of nanoindentation test data. Surf. Coat. Tech. 200(14), 4153 2006CrossRefGoogle Scholar
23Oliver, W.C.Pharr, G.M.: Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19(1), 3 2004CrossRefGoogle Scholar
24Troyon, M.Lafaye, S.: About the importance of introducing a correction factor in the Sneddon relationship for nanoindentation measurements. Philos. Mag. 86(33), 5299 2006CrossRefGoogle Scholar
25Doerner, M.F.Nix, W.D.: A method for interpreting the data from depth-sensing indentation instruments. J. Mater. Res. 1(4), 601 1986CrossRefGoogle Scholar
26Joslin, D.L.Oliver, W.C.: New method for analyzing data from continuous depth-sensing microindentation tests. J. Mater. Res. 5(1), 123 1990Google Scholar
27Gindl, W.Schoberl, T.: The significance of the elastic modulus of wood cell walls obtained from nanoindentation measurements. Composites Part A: Appl. Sci. 35(11), 1345 2004CrossRefGoogle Scholar
28Slaughter, A.E.: Design and Fatigue of a Structural Wood–Plastic Composite Washington State University Pullman, WA 2004Google Scholar
29Hull, R.: Properties of Crystalline Silicon IEE 1999 xxvi+1016Google Scholar
30Stillwell, N.A.Tabor, D.: Elastic recovery of conical indentations. Proc. Phys. Soc. 78(2), 169–179 1961CrossRefGoogle Scholar
31Sakai, M.Nakano, Y.: Elastoplastic load–depth hysteresis in pyramidal indentation. J. Mater. Res. 17(8), 2161 2002CrossRefGoogle Scholar
32Warren, O.L., Dwivedi, A., Wyrobek, T.J., Famodu, O.O.Takeuchi, I.: Investigation of machine compliance uniformity for nanoindentation screening of wafer-supported libraries. Rev. Sci. Instrum. 76(6), 62209 2005CrossRefGoogle Scholar
33Grillo, S.E., Ducarroir, M., Nadal, M., Tournie, E.Fauriel, J.P.: Nanoindentation of Si, GaP, GaAs and ZnSe single crystals. J. Phys. D: Appl. Phys. 36(1), 5 2003CrossRefGoogle Scholar
34Vlassak, J.J.Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42(8), 1223 1994CrossRefGoogle Scholar
35Hall, J.J.: Electronic effects in the elastic constants of n-type silicon. Phys. Rev. 161(3), 756 1967CrossRefGoogle Scholar
36Cramer, S., Kretschmann, D., Lakes, R.Schmidt, T.: Earlywood and latewood elastic properties in loblolly pine. Holzforschung 59(5), 531 2005CrossRefGoogle Scholar
37Jakes, J.E., Hermanson, J.C.Stone, D.S.: Nanoindentation of the interphase region of a wood-reinforced polypropylene composite in Proceedings of the Ninth International Conference on Woodfiber-Plastic Composites, (Madison WI, 21–23 May, 2007), pp. 197–203Google Scholar
38Gerber, C.E.: Contact Problems for the Elastic Quarter-Plane and for the Quarter Space Stanford University Palo Alto, CA 1968 100Google Scholar
39Hetenyi, M.: Method of solution for elastic quarter-plane. Trans. ASME Series E, J. Appl. Mech. 27(2), 289 1960CrossRefGoogle Scholar
40Hetenyi, M.: A general solution for the elastic quarter space. Trans. ASME Series E, J. Appl. Mech. 37(1), 70 1970CrossRefGoogle Scholar
41Keer, L.M., Lee, J.C.Mura, T.: Contact problem for the elastic quarter space. Int. J. Solids Struct. 20(5), 513 1984CrossRefGoogle Scholar
42Popov, G.Y.: An exact solution of the mixed elasticity problem in a quarter-space. Mech. Solids 38(6), 23 2003Google Scholar
43Schwarzer, N., Hermann, I., Chudoba, T.Richter, F.: Contact Modelling in the Vicinity of an Edge Elsevier San Diego, CA 2001 371–377Google Scholar